picos.expressions.exp_sumxtr¶
Implements SumExtremes
.
Classes¶
SumExtremes¶
-
class
picos.expressions.exp_sumxtr.
SumExtremes
(x, k, largest, eigenvalues=False)[source]¶ Bases:
picos.expressions.expression.Expression
Sum of the
largest or smallest elements or eigenvalues.
- Definition
Let
.
If
is an
-dimensional real vector or matrix and
eigenvalues == False
, then this is the sum of thelargest or smallest scalar elements of
, depending on the truth value of
largest
.Special cases:
If
, this is either the largest element
or the smallest element
of
.
If
, this is the sum of all elements
of
.
If
is an
hermitian matrix and
eigenvalues == True
, then this is the sum of thelargest or smallest eigenvalues of
, depending on the truth value of
largest
. Recall that the eigenvalues of a hermitian matrix are real.Special cases:
If
, this is either the largest eigenvalue
or the smallest eigenvalue
of
.
If
, this equals the trace
.
If the given
exceeds the
of either case, then
is silently clipped to
.
-
__init__
(x, k, largest, eigenvalues=False)[source]¶ Construct a
SumExtremes
.- Parameters
x (ComplexAffineExpression) – The affine expression to take a sum over.
k (int) – Number of summands.
largest (bool) – Whether to sum over the largest (eigen)values as opposed to the smallest.
eigenvalues (bool) – Whether to sum eigenvalues instead of elements.
-
property
eigenvalues
¶ Whether the sum concerns eigenvalues as opposed to elements.
-
property
full
¶ Whether the sum concerns all (eigen)values of the expression.
-
property
k
¶ Number of (eigen)values to sum.
-
property
largest
¶ Whether the sum concerns largest values as opposed to smallest.
-
property
x
¶ The expression under the sum.